Analytic determination of dynamical and mosaic length scales in a Kac glass model

TL;DR

This paper analytically computes dynamic and static length scales in a disordered spin glass model with long-range interactions, revealing their divergence at phase transitions and a crossover in dynamical behavior.

Contribution

It introduces a method to determine dynamic and static length scales in a Kac spin model, highlighting their divergence and the crossover from mode coupling to activated dynamics.

Findings

Length scales diverge at phase transitions with specific exponents

The two length scales are approximately equal above the mode coupling transition

Discrepancy between length scales increases near the transition

Abstract

We consider a disordered spin model with multi-spin interactions undergoing a glass transition. We introduce a dynamic and a static length scales and compute them in the Kac limit (long--but--finite range interactions). They diverge at the dynamic and static phase transition with exponents (respectively) -1/4 and -1. The two length scales are approximately equal well above the mode coupling transition. Their discrepancy increases rapidly as this transition is approached. We argue that this signals a crossover from mode coupling to activated dynamics.